Yes. The temperature of your food will not affect your pregnancy.
Yes. Yes you can drink.
Yes. No one, especially pregnant women and children, should drink hot water from the tap or lead pipes. Beside that, in general, guidelines would be similar for someone who is not pregnant. Obviously water should be cool enough that the lining of the mouth is not harmed. The herbs, plants, flavors added to the water should not be toxic. Common sense must be used to avoid spilling and scalding.
Yes. The temperature of the water you drink (cold, cool or warm) will not harm you or the baby. Hot water may scald or burn you--so be careful! if you were to swallow hot water ( for example, from coffee or tea) that is not too hot to hurt you, it will not harm your baby.